Category:General Relativity (GR)

General Relativity (GR)

Albert Einstein's General Theory of Relativity (GTR, General Relativity, GR) was published in 1916, as "The Foundation of the General Theory of Relativity" ("Die Grundlage der allgemeinen Relativitätstheorie").

The core concept of a general theory of relativity is the general principle of relativity (GPoR), the idea that the principle of relativity does not only apply in the obvious case of simple inertial motion in straight lines, but can also be applied to the case of systems that include rotating and physically accelerated masses, as suggested in the late C19th by by Ernst Mach.

Contents

Iterations

GR1916

Einstein's actual general theory of relativity. Principle-based, but internally logically inconsistent, due to the conflict between SR and the GPoR.

GR1960

The amended version of the theory that became standard after the 1960 crisis. This gives SR priority over the GPoR, and says that when the two appear to collide, the GPoR is to be suspended. No longer a principle-based theory (in the sense of the GPoR). GR1960 is not compatible with quantum mechanics.

"Credible" GR alternatives, 1970s textbooks

GR1960 is compared against a number of other "variations on a theme", with the differences testable using the PPN (Parameterised Post Newtonian) framework. However, since all theories accepted as "credible" alternatives are required to be a full superset of SR, presumably the SR component means that none of them fully support the GPoR, or have QM compatibility.

Advanced General Relativity

The result of applying the general principle of relativity without presupposing the validity of special relativity. This gives a theory that reduces to a relativistic acoustic metric rather than to the Minkowski metric of special relativity. Although this class of theory merges and simplifies some areas of inertial/gravitational physics and appears to be QM-compatible, and the mathematics is a legitimate field of study for QG researchers, it is not compatible with C20th classical physics peer review, which demands full SR-compliance. "Pure GR" lies outside the theory-space mapped by PPN and other mainstream C20th classification systems.

Development of General Relativity, timeline

Pre-C20th

Seventeenth Century – Isaac Newton describes gravitational effects as being the result of a variable-density medium, which deflects light and matter towards the regions of higher mass-density as a "refractive" effect. Newton's concept can be considered a curved-space model. Newton unfortunately makes a mistake and inverts a series of relationships, with the result that his medium has to be displaced by the gravitational field, instead of being the gravitational field (as it us under Einstein's general theory).

Late Eighteenth Century – John Michell publishes the result that the energy of light must change as it crosses a gravitational gradient (gravitational shift). He also calculates the critical r=2M radius for stars whose surface gravity is strong enough to trap light (dark star / black hole).

Early Nineteenth Century – Confusion over Newton's mistake causes an unpleasant rift between Continental physicists who use wave theory to generate the correct relationships, and English physicists who stick to the faulty Newton predictions and dismiss the wave approach. At the beginning of the century, experiment supports the wave-based arguments, and the ensuing embarrassment means that Newton's Opticks goes out of print, and Michell's paper (which referenced the mistake) disappears from the citation chain (Newtonian Catastrophe).

Late Nineteenth Century – Since all bodies fall at the same rate in a gravitational field, and Eotvos' principle requires light to be deflected according to the same rules, we can map a region affected by gravity using lightbeams, and use the resulting "warped" map as a description the region's true geometry – instead of talking of a gravitational field defecting nearby bodies, we can talk of the curvature of space deflecting bodies.

This approach is tried (unsuccessfully) in the late C19th by Gauss and Riemann, who develop the geometrical theory of curved surfaces in multiple dimensions.

Ernst Mach proposes that "relativists" believe that all forms of motion are purely relative, including rotation and acceleration. The forces that are usually interpreted as showing that one has absolute motion, says Mach, can be explained as the result of a special type of gravitational field effect that appears when bodies have relative acceleration of rotation.

Early C20th

1905 - Einstein's special theory of relativity loosens the concept of timeflow.

1911 – Einstein rediscovers the Michell argument for gravitational shifts, and extends it – when light gains energy falling downhill, the energy-change must be manifested as an increase in frequency, which leads to nonsensical results unless the rate of timeflow is also physically different in different gravitational environments ...

... this means that gravitation does not just appear to warp space, it also warps time. This realisation that a geometrical theory of gravity has to operate in four dimensions rather than three is "the missing piece of the jigsaw" required for a workable geometrical theory of gravity. After 1911, the race is on to see who can produce the first working example.

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Imagine a coordinate system which is rotating uniformly with respect to an inertial system in the Newtonian manner. The centrifugal forces which manifest themselves in relation to this system must, according to Newton's teaching, be regarded as effects of inertia. But these centrifugal forces are, exactly like the forces of gravity, proportional to the masses of the bodies. Ought it not to be possible in this case to regard the coordinate system as stationary and the centrifugal forces as gravitational forces? … This hasty consideration suggest that a general theory of relativity must supply the laws of gravitation ...

Einstein works on an extended theory of relativity, guided by Mach's arguments. Relative rotation must generate dragging effects between the two relatively-rotating systems, and forced relative acceleration of a body must warp the surrounding region. When an accelerated body feels apparent gravitational fields, for them, those fields are real.

Faced with the daunting task of having to rewrite the laws of physics to take curvature effects into account, Einstein has the happiest thought of my life – A person in a laboratory freefalling in a gravitational field feels no gravity - for them the background gradient does not appear to exist, and the inertial physics inside the lab appears the same as if they were drifting in space. So "gravitational" physics has to reduce over small regions of spacetime to inertial physics.

Einstein already has a theory of inertial physics – special relativity – so he has his new theory reduce to SR physics as a limiting case.

1915/1916 – While existing Newtonian theory predicts lightbending and a precession of Mercury's highly elliptical orbit, Mercury actually precesses more than expected under C19th NM. Einstein uses this as a guide, and gets the theory to predict the stronger precession value in ~1915. When the theory's bugs are ironed out in 1916, and the desirable precession prediction is found to still be intact, Einstein declares the theory finished, and publishes it (having already announced it in late 1915).

1919 – Under Einstein's theory of curved spacetime, lightbeams are bent by twice as much as under C19th Newtonian theory, because of the additional time-curvature effect - although we could calculate time-warpage from Newtonian arguments (Einstein 1911) and update Newtonian theory to match, researchers capable of doing this are more interested in post-Newtonian approaches. A team led by Arthur Eddington sets out to measure the effect of the Sun's gravity on starlight during an eclipse, and reports a confirmation of Einstein's 1916 prediction.

After the misery of World War One (1914-18) the idea that a German theorist and an English experimenter (both pacifists, from opposing sides of the conflict) had just cooperated to overthrow the previous system of physics catches the interest of a public desperate for optimistic news, and Einstein becomes famous.

Einstein spends the ensuing years until his death in 1955 arguing about quantum mechanics and trying to further extend or improve the general theory. Perhaps the repugnant idea of a one-way gravitational event horizon can be eliminated, perhaps the theory can be rewritten to make it cleaner, perhaps it can be extended to include other forces and create a "Unified Field Theory"?

1950 - Einstein goes on record as saying that he no longer considers his original decision to incorporate special relativity in GR to be correct. The approach is the best that had been possible in 1916, but is no longer defensible with hindsight, as seen from the perspective of 1950. It is not correct to limit GR arguments to explicitly "gravitational" physics, in the hope that everything else can be dealt with by SR. Almost nobody pays any attention.

Late C20th

1955 Einstein dies.

The 1960 Crisis, it is realised with a shock, that not only is SR not provably compatible with the GPoR, it's provably incompatible with it. This puts the community in a quandary. The correct thing to do would seem to be to rewrite GR without assuming SR (as suggested by Einstein), but this would mean that GR1916 and special relativity are BOTH wrong. The community would lose both current C20th theories of relativity and have to start over, knowing that there is currently no obvious research project for a replacement GR, that nobody knows how long it might take to write a replacement, and that the world expert in these matters is now dead, having warned the community of a potential problem and been ignored.

GR1960 – it is decided that SR is "too big to fail". Since losing SR is unacceptable, it is easier to keep the structure of GR1916, downgrade the GPoR to a guideline rather than a law, and state that whenever the GPoR and SR are about to collide, SR should be given priority. This converts GR to a constructive theory, but allows theological consistency. Full SR-compliance is announced as being compulsory for all credible gravitational theories.

~1960 – John Archibald Wheeler starts his "geometrodynamics" research program, which he describes as continuing the work of Einstein and Clifford. It is conceivable that that this programme may be a "black programme" intended to study "pure" non-SR GR arguments, but if so, it doesn't manage to produce an alternative general theory.

1960s-1970s. The research community becomes excited by the subject of GR black holes. GR1960 becomes supported in textbooks with new retrospective definitions and laws that make full SR-compliance a compulsory part of any gravitational theory that is to be considered viable, eliminating any competing research on "pure" GR. GR1960 is declared to be the "Gold Standard" in gravitational theory, and any theory that is not effectively "GR1960 with variations" is ruled out. A list of criteria is produced that any competing theory has to meet in order to be considered even worth testing, which include compatibility with QM ...

1970s ... unfortunately, in the mid-1970s it is realised that Stephen Hawking's prediction of Hawking radiation makes SR-centric GR1960 incompatible with QM. According to MTW's rules designed to defend GR, the 1960 theory is now "not even worth testing".

C21st

Quantum gravity researchers study acoustic models as "toy models" of the behaviour of a potential future theory of quantum gravity, but are not able to present their work as a possible competitor to GR19160, as it is not 100% SR-compatible.